In a manufacturing factory, accurate and consistent performance assessment from sub-assembly and assembly floors is critical to design engineers' ability to optimize product design, as well as to manufacturing engineers' ability to control the process to maintain quality of the outgoing product. In some systems, a product's performance is assessed throughout the product life cycle, from development to volume production, using data management systems that provide a number of performance parameters, such as Yield, Cpk, Xbar-S and Xbar-R charts. However, traditional data management systems are typically based on an assumption that data is distributed according to a normal distribution.
In practice, this assumption often fails due to the existence of outlying data points. Outlying data points may give rise to a mixed population data set, i.e., a single data set containing subsets of data that each fit a different distribution, in which each data subset may need to be separately analyzed. Moreover, many distributions are so highly skewed that even a large sample size (e.g., 30) is not enough to make the data normally distributed. In this case, the data may be better described by a probability density function (PDF) other than the normal distribution, such as a Weibull distribution, a Laplace distribution, an exponential distribution, or other distribution.
The design phase of product development may implement “scorecards” as a management tool. Scorecards display a list of important parameters, referred to as “Critical to Quality” (CTQ) parameters. Product sub-system design teams and process development teams each have respective scorecards. Each team collects performance CTQ raw data, and manually analyzes the raw data to obtain a process capability Z-score for each CTQ parameter for their respective scorecards. At various phases of the design cycle, the scorecards are assessed to ensure Z-scores meet minimum requirements. Design changes may then be made to improve upon those CTQ parameters with unacceptable Z-scores. As design changes tend to be costly and sometimes affect the time-to-market of a product launch, the accuracy of the scorecard data analysis becomes a critical factor in the design change decision-making process.
One example of a process control and triggering system calculates triggers based on a parameter known as Cpk. Cpk is a measure of the capability of a process. The traditional formula for Cpk assumes that data is normally distributed, and so a computed value of Cpk is only accurate if the data is normally distributed. If the data does not follow a normal distribution, the Cpk may over-estimate or under-estimate the capability of a process, triggering false quality alerts and potentially wasting resources. Due to the assumption of normality, existing statistical software used for product performance assessment in quality control systems may result in inaccurate performance assessment, high false trigger rates, and insensitivity to quality control problems.